Straight Tack: AKA Back Tack, Beginner Tack, The video shows the rider taking his back foot out of the strap before starting the tack. Most riders do not do this. Having the back foot in the strap allows you to push the rear of the board around easier since your foot is further aft. It also keeps you in contact with the board longer for better control, and keeps your speed up going into the tack. I'm not the greatest at tacking but I think most of the good riders would agree. Having said this, I remember taking my back foot out when I was starting to work on tacks. It seemed to help in the beginning when attempting tacks in super smooth water.
Gybe: Most riders downloop the kite during the gybe instead of bringing it up and over. Maybe Flysurfer riders don't do this.